1. Introduction

Breast cancer is still the leading cause of cancer-related deaths for women worldwide [1,2]. Utilization of elastographic imaging based of medical ultrasound (US) has been widely used for characterization of focal breast lesions. The advantage of elasticity imaging is based on the fact that most soft tissues share similar ultrasonic echogenicities but may have significantly different shear/Young’s moduli, which can be used to clearly delineate pathologic lesions from normal tissues. In the breast, cancers tend to be stiffer than benign lesions, and it has been reported that in comparison with conventional structural imaging ultrasound-based elastography can significantly improve the accuracy of diagnosis of solid lesions in breast tissue [3,4].

Similarly, to ultrasound elastography (USE) the emerging Optical Coherence Elastography (OCE) develops in two main directions: (i) the wave-based elastographic techniques [5] and (ii) quasistatic techniques based on the compression principle (e.g. [6–12] and review [13]). Recently, the first study has been reported on side-by-side comparison of wave-based OCE and wave-based USE using phantoms in highly controllable conditions [14]. Both techniques were shown to enable well consistent quantitative estimates of shear (or Young’s) moduli.

Until present there were no similar comparative studies of compression OCE (C-OCE) and compression US-elastography. This comparison may be rather non-trivial because the two techniques enable the elastographic information in essentially different forms. We recall that in quasi-static C-OCE, due to application of pre-calibrated reference layers, it is possible to quantify both the Young’s modulus [9,15], as well as stress for which this modulus is estimated [16–18]. This feature makes it possible to eliminate uncontrollable (possibly rather strong) variations in the modulus of the tissue caused by its intrinsic nonlinearity [3,16]. Another feature is that in comparison with ultrasound elastography the optical C-OCE enables significantly higher resolution [19], which is especially important for studying intrinsically heterogeneous breast tumors [20].

Further, in contrast to C-OCE enabling quantitative estimates of the elastic modulus, compression-based ultrasound elastography visualizes only strain distribution and by this reason is also often called ultrasound strain elastography (US-SE) [21–23]. This strain is produced by uncontrollable stress exerted on the tissue by the compressing ultrasound probe. Therefore, due to intrinsic nonlinearity and inhomogeneity of real tissues the reconstructed strain distribution only indirectly corresponds to the distribution of the Young’s modulus in the visualized region. In US-SE the difference in elasticity for different tissue types is characterized by the so-called elasticity score corresponding to the ratio of the strains in the compared zones (tumor and its vicinity). This ratio has proven to be rather helpful for breast lesion characterization in clinic and has been widely used to differentiate benign and malignant lesions with sensitivity and specificity of 83–93% and 84–95% respectively [24–27]. Numerous studies are known that demonstrate similar diagnostic performance of strain and shear-wave US elastography of breast masses. Both of these techniques significantly improved the diagnostic efficiency of medical ultrasound compared with conventional B-mode (structural) US imaging [28–32]. However, US strain elastography has several limitations because the acquired information is operator dependent and enabling only relative characterization of the tissue elasticity. Moreover, the resolution of this method is not sufficient to detect negative resection margin within 1–2 mm of the tumor vicinity as required for intraoperative control. Thus, new high-resolution and intraoperatively applicable technologies are needed to improve the results of breast-conserving surgery (BCS).

For early stage breast cancer, BCS is the preferred surgical intervention in which of key importance is to achieve clear (or negative) tumor margins to exclude additional surgery in the form of re-excision or mastectomy [33,34]. Currently, there have been several intraoperative tools for breast tumor margin assessment (frozen section and imprint cytology), but these techniques require rather long procedure times and suffer from sampling rate limitation [35–37]. Therefore, a need exists in developing an intraoperative margin assessment tool that is rapid, accurate, and able to examine the near-surface tissue region with a high resolution and in (nearly) real-time.

In this regard, interesting prospects offers the recently developed technique based on phase-sensitive realizations of compression OCE enabling quantitative elastographic evaluation of tissue samples of ∼cm sizes with detail on a micron level scale, which cannot be offered by elastography based on the competing imaging modalities - US and MRI. In previous studies, we have shown that C-OCE technique is able to provide images with micro-scale mechanical contrast, enabling us to distinguish benign from malignant tissue and different morphological/ molecular breast cancer subtypes in freshly excised human breast tissue [20,38]. It was shown, that OCE is a promising method for intraoperative guidance during the resection of breast cancer and for identifying positive margins in specimens from BCS [39,40].

Here we report the first comparative study the two different methods, US-SE and C-OCE, both of which basically share the same compression elastography principle. The aims of this study are: (i) to verify consistency of US-SE and C-OCE results using elastically linear homogeneous phantoms similarly to the recent comparison of the wave-based counterparts of OCE and USE in [14]; (ii) to evaluate factors that can affect the results of the two elastographic techniques obtained for real inhomogeneous and elastically nonlinear breast-cancer tissues; (iii) to compare the results of US-SE with C-OCE in differentiating benign and malignant (of various grades) lesions for the same breast masses, as well as to apply C-OCE for intraoperative search for clean resection margins with histological verification.

2. Materials and methods

2.1 Patient selection and data collection

The present study was approved by the institutional review board of the Privolzhsky Research Medical University. All of the patients included in the study provided written informed consent. Breast US-SE was performed on 22 patients (age range, 21–79 years) who exhibited 24 breast lesions. Of the 24 lesions, 5 (20%) were benign and 19 (80%) were malignant. The sizes of those lesions according to the US examinations ranged from 0.5 cm to 2.0 cm. All lesions were under went subsequent surgical excision and histological examinations. For all breast cancers, a breast-conserving surgery was performed. The tumor grade, its histological type, and invasive tumor size were determined by histological examination of the surgically resected specimen.

C-OCE images of the fresh, un-fixed breast tissue specimens were acquired within 1 hours after surgical excision. Specimens were taken from central zone of tumors. Figure 1 shows the schematic of US-SE examinations of lesions in breast and corresponding of breast-tissue sample prepared for C-OCE examination. The studies were done on specimen with sizes from 0.5 × 1.0 cm to 1.0 × 2.0 cm. The entire C-OCE study of each specimen was no longer than 5 minutes (including preliminary sample preparation and orientation). Histopathology results were obtained for all patients after surgical excision samples.

 

Fig. 1. (a) Schematic of US-SE examinations of lesions in breast; (b) photo and schematic of breast-tissue sample prepared for C-OCE examination; (c) schematic of C-OCE examination of the tumor and surrounding peri-tumorous region utilizing stitching of elastographic scans. The C-OCE detection line represents the acquisition direction of sequential elastographic scans.

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2.2 Ultrasound strain elastography (US-SE) imaging

Conventional B-mode ultrasound scans and compression elastography (“strain elastography”) images were obtained using a medical scanner (RS-80A, Samsung Medison, Seoul, Korea) with a 3–12-MHz linear transducer, with resolution of 500 µm in the B-mode and scanning depth of 4-5 cm. For strain elastography, the target lesion was slightly compressed by the transducer in the direction of the sounding-beam axis. This compression caused the lesion straining and can be compared with straining of surrounding tissues to obtain semi-quantitative information about the difference in their elastic moduli. Real-time strain maps were visualized using a 256-color palette corresponding to the degree of strain; blue color corresponded to stiff tissue (least strain) and red represented soft regions (greatest strain). The elasticity score on strain elastography (“Tsukuba score”) is considered as a standard for breast cancer diagnosis [41]. The elasticity scores on a 5-point scale were estimated prior to surgical resection. The five-point scale is used to classify elastography patterns from benign to malignant as follows: score 1 for soft strain nodule with the entire lesion colored in green (benign), score 2 for lesion with a mosaic pattern of green, red and blue (probably benign), score 3 for a lesion with blue color in the middle and green in the periphery (benign or malignant are equivocal), score 4 for stiff strain nodule with the entire lesion colored in blue without surrounding area (malignancy suspected), and score 5 for stiff strain lesions with a blue surrounding area (malignancy strongly suggested).

Semi-quantitative approach was used to obtain a more objective and less operator-dependent free-hand technique for the identification of benign and malignant lesions by comparing the difference of the elastic response of the lesion and surrounding normal (fat) tissue, (i.e., “lesion-to-fat strain ratio”) [30,41,42]. The compared regions of interest were chosen on the obtained 2D strain images provided by US-SE (see Fig. 3(c)). The size of each region of interest was 10 × 10 mm by default. Then the strain ratio was estimated for the chosen regions of fat and the lesion. Stachs et al. [43] demonstrated that the strain ratio was predominantly higher in malignant tumors (≥3.04) versus in benign tumors (≤1.91).

2.3 Compression optical coherence elastography (C-OCE) imaging

We used a common path spectral domain OCT system with a central wavelength of 1.3 µm and spectral width of 100 nm, axial resolution of 10 µm, lateral resolution of 15 µm, and scanning depth of 2 mm in air and up to a depth of ∼1.5 mm in biological tissues because of higher refractive index of the latter. The rate of acquiring spectral fringes was 20 kHz.

The principles of realized phase-sensitive compression OCE were described in [13,16,18,44–47]. The axial interframe strain was estimated by finding axial gradients of interframe phase variations. To estimate the phase-gradients we used the “vector” method proposed in [46,47]. The name “vector” relates to the fact that the complex-valued OCT signals in this method are treated as vectors in the complex plane. The phase is explicitly singled out only at the last step of signal processing. Finding the phase gradients using this method obviates the necessity of phase unwrapping even for supra-pixel displacements of scatterers. The intrinsic feature of vector method is its ability to suppress especially strong phase errors (by ∼π rad.). The vector representation also allows for flexibly-tunable amplitude-weighted averaging over the chosen processing window. Due to this, contributions of noisy small-amplitude pixels can be efficiently suppressed. These features confer to the vector method exceptional robustness with respect to various noise including the strain-induced “decorrelation” noise. These features make it possible to obtaining strain maps of a decent quality even without periodic averaging. This is very important for one-directional loading of the tissue required for obtaining nonlinear stress-strain curves in a fairly broad strain range. An additional advantage of the vector method is its high computational efficiency, which requires only several seconds for elastographic post-processing of the OCT scans acquired during the tissue deformation. Furthermore, even real-time realization of elastographic imaging can be enabled using a “typical” desktop or even laptop computer without the necessity of parallel computations on multi-core graphical cards [48].

Concerning the resolution of the so-obtained strain maps, it can be said that it is inevitably lower than for initial structural scans. The main factor determining the resolution is the size of the processing window, over which the estimated phase-gradient is averaged. For a rectangular processing window with comparable axial and lateral sizes, the resolution in these directions is also comparable and roughly corresponds to ∼½ of the window size. For the used OCE system, the window size was ∼90–100 µm (chosen empirically as a compromise between lower quality of the OCE-images for too small averaging windows and too strong smoothing of spatial inhomogeneities for too large windows).

The above-described method of OCT-based mapping of local strains made it possible to quantify the tissue elasticity due to the application of translucent layers with pre-calibrated elasticity (usually made of silicones). Such a reference layer is placed between the studied tissue and compressing window of the OCT probe. It was experimentally verified that in contrast to real biological tissues silicones demonstrate highly linear elastic behavior in the strain range up to 40–60% [15,16,47]. Due to this fact, the comparison of strains in the reference layer and tissue makes it possible to obtain local stress-strain dependences which are usually pronouncedly nonlinear for the majority of real tissues [3,15,16,47]. Therefore, the current Young’s modulus (i.e. the slope of the stress-strain dependence) of the tissue may vary several times even for moderate strains on the order of a few per cent (or, correspondingly, within a stress range of several kPa). Consequently, meaningful quantitative interpretation of the estimated Young’s moduli for different measurements requires that these measurements should be made under either the same stress or strain of the tissue. In practice, it is more convenient to maintain the same stress using the reference silicone layer. The use of reference layers and full-optical standardization of the applied stress are described in detail in [15,16]. This is of key importance for the present study. We emphasize that even for different regions within the very same B-scan, the stress may vary up to several times, which impedes direct comparison of the moduli in these regions. However, by analyzing a series of sequentially acquired B-scans of the compressed tissue and using the reference silicone layers as optical sensors of local stress it is possible to derive the elasticity map for the same pre-chosen stress level over the entire area of such a synthesized OCE-image. This method gave the possibility to quantitatively compare the Young modulus even for samples with different uneven thickness and potentially strongly variable stiffness over the frame. For the presented below quantitative estimates of Young’s modulus, we used the stress range from 1 kPa to 3 kPa centered at 2 kPa. The stress was estimated by measuring the strain of the reference silicone layer. The application of reference silicone layers was discussed in detail in our previous publications [15,16,18,47]. Besides serving as optical sensors of stress, such a layer of soft silicone ∼300–500 µm in thickness also serves to fill and smooth irregularities at non-ideally planar surfaces of the samples. The importance of this issue and strong artefacts arising in the strain distribution due to direct contact of rigid surface of OCT-probe and a wavy tissue surface are specially discussed in [13].

Finally, we emphasize that, in contrast to invasive and time-consuming histology, OCE examinations can be made during several minutes directly on freshly excised tissue samples without special preparation and without any exogenous staining.

2.4 Histological study

After conventional in vivo US-SE imaging and ex vivo C-OCE imaging of the freshly-excised sample the area of OCE-scanning was marked on the specimen with histological ink. Then the specimen was fixed in 10% formalin for 48 hours and cut through the marked area to prepare the histological sections nearly coinciding with the plane of the C-OCE images. For the histological evaluation, haematoxylin and eosin (H&E) staining was used. Highly trained histopathologist (S.K.) interpreted the histological slices photographed in transmitted light with a Leica DM2500 DFC (Leica Microsystems, Germany) microscope. Based on histopathological analysis, all 24 breast lesions were classified: benign fibroadenoma (n = 5); grade I-II or low-grade infiltrating ductal carcinoma (IDC) (n = 10); grade III or high-grade IDC (n = 5) and grade III or high-grade infiltrating lobular carcinoma (ILC) (n = 4).

The results of histopathology were compared with the corresponding C-OCE-based findings. In all cases attention was given to investigating the differences in cellularity or composition between the central and peripheral portions of the tumor and surrounding marginal area. Findings of histologic grades of IDCs and ILCs, fibrosis, hyalinosis, lymphocytic inflammation and necrosis in the tumor were described.

2.5 Statistical analysis

For statistical analysis, we examined the mean stiffness values on C-OCE and mean strain ratio on US-SE of all benign and malignant lesions and those between histologic grades of IDCs and ILCs were also compared. Totally we studied 24 breast lesions. Because of larger sizes of US-SE images compared to C-OCE scans we acquired 2–3 C-OCE images from various positions on the sample corresponding to a single US-SE image. Correspondingly, the number of data points for C-OCE was greater than for US-SE (see Fig. 9).

Receiver operating characteristic (ROC) curves for C-OCE and US-SE images were analysed to evaluate diagnostic performance (sensitivity and specificity) and to compare the performances of established strain ratio categories and stiffness values. The best cutoff points yielding the maximal sum of sensitivity and specificity for C-OCE and US-SE were calculated. To summarize the overall performance, areas under the ROC curve (AUCs) were calculated and compared between these techniques.

The statistical analysis, including the estimations of sensitivity and specificity and plotting ROC curves, was performed using with a public domain software Prism v8 software (GraphPad Software, La Jolla, California).

3. Results

3.1 Comparison of US-SE and C-OCE for linear homogeneous phantom samples

Before performing comparison of US-SE and C-OCE for essentially inhomogeneous and elastically nonlinear real tissues it is very important to verify the consistency of these two techniques for linearly elastic, homogeneous phantoms. In our previous it was verified that soft silicones can be used for preparing phantoms with rather linear elastic behavior. Then for sandwich sample made of such linear materials with Young’s moduli $E_{}^{(1)}$ and $E_{}^{(2)}$, the incremental stress $\Delta P$ produced by the compression should cause incremental strains $\Delta \varepsilon _{}^{(1)}$ and $\Delta \varepsilon _{}^{(2)}$ independently of the current stress P created in the sample, such that

Therefore, for linear materials with stress-independent moduli, their ratio should be equal to the inverse ratio of the strain increments:

Furthermore, for a pair of linear materials with differentstress-independent moduli, ratio $E_{}^{(1)}/E_{}^{(2)}$ should be constant and should correspond to the ratio of cumulative strains:

It is important that the validity of Eq. (3) can be verified experimentally and can be used for verification of linearity of silicones using only strain measurements without the necessity of independent measurements of the applied pressure (stress). Indeed, if moduli $E_{}^{(1)}$ and $E_{}^{(2)}$ strongly differ (say, 5–10 times), then for the stiffer material within the initial strain range about several per cent, the deformation has linear character. Simultaneously the strain of the softer material is much higher (may reach tens per cent), where deformation of the material potentially may become pronouncedly nonlinear. This nonlinearity should break the linear proportion of the cumulative strains represented by Eq. (3). However, the experiments show that for silicones, the linear proportionally given by Eq. (3) remains valid up to several tens per cent [15,16,47]. This fact proofs that silicones are highly linear materials, for which the cumulative strain is proportional to the produced uniaxial stress. Therefore, silicones can be used as optical sensors of stress and plotting cumulative strain of silicone against cumulative strain of the tissue one readily obtains the stress-strain dependence which appears to be pronouncedly nonlinear for most of real tissues.

 

Fig. 2. Comparison of US-SE and C-OCE using sandwich-type phantoms made of linearly elastic homogeneous silicones with different Young’s moduli. (a-c) show the schematic of US-SE examination, structural B-scan and elastographic strain map, respectively. Panels (d-f) are the similar images for OCE, where in the elastographic map (f) the left half shows the “instantaneous” interframe strain and right half corresponds to cumulative strain. (g) shows the cumulative strains the two layers plotted one against another. (h) are the dependences of strains in each layer plotted against the compressing force measured by a force cell (layer A is softer with E∼100 kPa and the lower stiffer layer has E∼420 kPa). (i) is the stiffness map showing the distribution of the Young’s modulus, which for the linear silicones, can be found using either Eq. (2) or (3) because for silicones, tangent and secant moduli do not differ.

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The standard medical ultrasound devices, in which compression elastography is realized, enable imaging of fairly small incremental strains, typically of the order of fractions of one per cent. Thus, the first step of comparison between US-SE and C-OCE was made for sandwich structure made of the same pair of homogeneous silicones, for which the Young’s modulus differed ∼4 times with the smaller modulus in the upper layer. For tests of US-SE, the layers in the prepared sandwich sample had a thickness of ∼25 mm and 20 mm and a scattering pigment was added to enhance the scattering of ultrasound. The experiment schematic is shown in Fig. 1(a) and the representative structural and elastographic images enabled by the used medical scanner RS-80A (Samsung Medison) are shown in Figs. 1(b) and 1(c). According to the performed ultrasonic measurements the strain ratio was estimated as ${r_s} = 0.23 \pm 0.05$. The medical scanner was intensively used for everyday examinations of patient in the clinic, so that it was not possible to get full access to the output signal and change the default size of the averaging window. Nevertheless, the plane-layered structure of the sample was clearly seen and the average estimated strain ratio for the layers demonstrated good agreement with the C-OCE results described below.

For C-OCE tests (schematic of which is shown in Fig. 2(d)), certainly the silicone layer thicknesses were much smaller, about 800 µm as is clear from the structural image Fig. 2(e). Figure 2(f) shows the corresponding interframe and cumulative strain maps obtained using the vector methods [46]. The left part of this panel shows the interframe strain map, whereas the right-hand part shows the cumulative strain that looks much smoother and less noisy. Indeed, summation of interframe strains for monotonic straining, similarly to averaging of periodic signals, helps to reduce alternating-sign noises [47], which is clearly seen from the comparison of the left- and right-hand halves of Fig. 2(f). In the next panel Fig. 2(g) the cumulative strains estimated from the C-OCE maps for the two layers are plotted one against another.

The resultant dependence in such sandwich-type tests with a high accuracy remains linear up to fairly large strain of several tens per cent [15,16,47]. The slope of the linear dependence (strain ratio) in Fig. 2(g) well agrees with ${r_s}$ estimated by US-SE and equals to 0.24 for the C-OCE data. As elucidated above, this linear proportionality even without direct stress measurements confirms the high elastic linearity of silicones. We note that in the examples shown in Figs. 2(g) and 2(h) the maximal strain in the softer layer was limited to 10% in order to avoid overload of the force cell that was used in parallel to directly measure the applied force. The force cell allowed us to independently verify the linear proportionality between the strain of each silicone layer and the applied stress (to estimate the latter, the applied force was divided by the area of the OCT probe). The corresponding stress-strain dependences for the two silicones are shown in Fig. 2(h). The slopes of these linear dependences correspond to the Young’s moduli for these silicone layers (they are estimated as $E_{}^{(1)} = 100$ kPa for the upper softer layer and $E_{}^{(2)} = 420$ kPa for the stiffer bottom layer). We emphasize that only due to linearity of the stress-strain dependences in Fig. 1(h) there is no difference between the estimated tangent and secant values of the Young’s modulus.

Therefore, the performed measurements of strains in the sandwich structure made of homogeneous and highly linear silicones demonstrate good agreement in the estimated strain ratios independently obtained using US-SE and C-OCE. However, despite this agreement we will show in the next section that for real tissues the estimated strain ratios by US-SE and ratios of the Young’s moduli obtained using C-OCE may differ very strongly for the very same compared real breast tissues.

3.2 US-SE strain ratio versus ratio of the elastic moduli determined by C-OCE for real breast tissues with intrinsic inhomogeneity and pronounced nonlinearity

The linearity of silicones ensures that their strain variations (both incremental and cumulative) are proportional to the corresponding variations in the applied stress. In view of this, such reference silicone layers can be used as optical sensors of the current local stress in C-OCE measurements. By plotting strain of the reference layer with known modulus against the strain of the examined tissue beneath this layer one obtains the stress-strain dependence of the tissue. Therefore, even if the stress may be inhomogeneous across the scan (because of mechanical inhomogeneity and nonlinearity of the tissue, imperfectly plane tissue surface or inclined orientation of the probe), it is still possible to estimate the tangent modulus for the same chosen stress over the entire OCE scan [16].

Standard medical devices with the US-SE modality have no such possibilities, so that the estimated strain ratio for spatially separated regions may correspond to noticeably different stress in the compared regions (there are many factors that may cause this difference, e.g., tilted orientation of the probe surface, internal mechanical inhomogeneity of the tissue, non-ideally planar surface of the latter). Even if the tissues were perfectly linear, solely this stress inhomogeneity over the scan could introduce noticeable uncertainty in the estimated ratio. Furthermore, the presence of nonlinearity may introduce additional uncontrollable uncertainty.

 

Fig. 3. Comparison of US-Se and C-OCE in the breast cancer examination. US-SE was made in vivo before surgery and then after surgery the excised samples from regions A and B were studied by C-OCE. (a, b) are schematics of US-SE and C-OCE examinations; (с, d) are the US-SE structural and elastographic images. (e, f) are the structural OCT scans for the regions labeled A and B in the US-SE scans. (g,h) are the C-OCE stiffness maps for regions А and B, respectively; (g1, h1) are the corresponding histological images of the tumor and adipose; (i) are the stress-strain curves obtained by C-OCE for regions A and B (the dashed lines are experimental measurements and solid lines are their approximations); (j) are the corresponding dependences of the Young’s moduli derived from the approximating curves in panel (i); (k) is the plane of two stresses (P_norma, P_tumor) and the curve along which the strain ratio equals 3.43, i.e., the value found in the US-SE examination without local stress control.

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Fig. 4. The surface showing possible ratios of the Young’s moduli for regions A (tumor) and B (adipose) from Fig. 3 plotted for various combination of stresses (pressures) P_norma and P_tumor. The dashed line shows the stress levels, for which the strain ratio corresponds to the value 3.43 found in the US-SE examination presented in Fig. 3.

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These statements are illustrated in Fig. 3 in which the US-SE images are obtained in vivo for a breast tissue in the region containing a lesion with increased stiffness. Figures 3(a), 3(b) and 3(c) represent the schematic of the US-SE examination, structural US image and elastographic US-SE image, respectively. The lesion corresponds to low-echogenicity zone in the structural image and blue region in the elastographic US-SE image). The estimated strain ratio for the two regions of interest shown by the circles is ${r_s} = 3.43$, which is typical of a malignant tumor that should be excised. After surgical excision the samples taken from the central zone of the tumor and normal tissue (adipose) at the periphery were subjected to C-OCE examination. Structural OCT images for these samples are shown in Figs. 3(e) and 3(f) and the corresponding C-OCE images in Figs. 3(g) and 3(h) (in the latter panels the overlying reference silicone layer is cropped).

The stress-strain curves for the tumor tissue and adipose are shown in Fig. 3(i). Figure 3(j) shows the corresponding dependences of the tangent Young’s modulus as a function of stress (the stress was estimated based on the measured strains of the reference silicone layer). The tangent Young’s modulus is obtained by differentiating the fitting curves for the experimental stress-strain curves shown in Fig. 3(i).

Looking at these plots it should be emphasized that, in contrast to silicones, the stress-strain curves in Fig. 3(i) for both tissue samples are nonlinear, especially nonlinear is the tumor tissue, for which the modulus increases over 4 times with increasing stress (in the range from ∼1 kPa to 14 kPa in this measurement). Second, Fig. 3(j) clearly shows that for any given stress, the ratio of the Young’s moduli for the tumor and adipose is much greater (∼3-10 times) than the strain ratio 3.43 given by the US-SE measurement. This apparent inconsistency between the C-OCE and US-SE measurements is explained by the combined effect of stress inhomogeneity over the scan and tissue nonlinearity. Ratio 3.43 may be observed, but only for significantly different stress applied to the adipose and tumor as is schematically shown in Fig. 3(j) for two of such stress combinations. Figure 3(k) presents the dependence corresponding to all combinations of stresses applied to the tumor and adipose, for which the ratio of tangent Young’s moduli equals 3.43. Stress inhomogeneity may often occur even over scales of several millimeters typical of OCE scans and this inhomogeneity potentially may be even stronger over much larger sizes of US scans. The tissues, for which the stress dependences are shown in Fig. 3(j), for all possible combinations of stresses realized experimentally may exhibit ratios of tangent moduli varying from 2.1 to 47.4 times as shown in Fig. 4. The combinations of stress levels corresponding to the ratio ${r_s} = 3.43$ of the incremental strains (and, therefore, tangent moduli) is shown by the dashed line in Fig. 4.

Therefore, despite the well coinciding strain ratios given by US-SE and estimated by C-OCE in the case of plane-layered homogeneous and linearly-elastic silicones, for real tissues with intrinsic nonlinearity and spatial inhomogeneity, there may be very pronounced difference between the results of US-SE and C-OCE. In the next sections we demonstrate how this difference affects the accuracy of diagnostic conclusions obtained by these two elastographic techniques.

3.3 Comparison of US-SE and C-OCE in the differentiation of benign and malignant breast lesions with examples of contradicting conclusions

To compare US-SE and C-OCE in the differentiation of benign and malignant breast lesions, we first used US-SE to image breast lesions before excision on patients undergoing surgical removal of breast tumors and then performed C-OCE examination of the freshly excised samples. For these samples, we obtained 2D C-OCE-based stiffness maps for the central zone of the tumor and compared them with similar stiffness maps for the peri-tumoral tissue.

Figure 5 corresponding to a benign fibroadenoma demonstrates the results of elastographic examinations by the two techniques that gave contradicting results. The fibroadenoma showed high strain ratio in US-SE images (Fig. 5(b)), which looked too high for a benign lesion and, therefore, lead to the false-positive conclusion about a malignant tumor. Indeed, this benign lesion according to the US-SE results showed an elasticity score of 4 a strain ratio of 3.92 (see US-SE images in Fig. 5(a) and 5(b)).

 

Fig. 5. Benign fibroadenoma (of a 21-year-old woman). (a) B-mode ultrasound scan shows hypoechoic nodule with regular and well-defined margins (green circle). (b) The US-SE image in which the color map score is between 3 and 4 according to Tsukuba score (due to the blue color in the lesion area), with a high strain ratio of 3.92. (c) quantified C-OCE image in which the lesion is mostly uniform and characterized by a fairly low Young’s modulus typical of fibrosis. (d) Histological images of a surgically excised specimen stained with H&E demonstrate excrescence of the fibrous stroma (FS) that squeezes the duct channels, so that the latter look as narrow fissures (marked by the arrows). The dashed line on the US-SE image in panel (b) shows the direction corresponding to the C-OCE and histological images.

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Figure 5(c) showing the elastic modulus map obtained by C-OCE indicates that the fibroadenoma is fairly heterogeneous, which is confirmed by histological slices Fig. 5(d), in which one can see the excrescence of connective tissue with the presence of large fibrous collagen bundles having a dense structure around mammary-gland structures with squeezed ducts that take the form of narrow gaps. These different components exhibit slightly different stiffness values in corresponding C-OCE images (Fig. 5(c)). The C-OCE image (Fig. 5(c)) visualizes increased stiffness (>200 kPa) in the region of the ductal and lobular structures, lower stiffness (<200 kPa) in the surrounding softer fibrous tissue of the fibroadenoma.

Thus, fibroadenomas with pronounced fibrotic component can have a suspicious color map in US-SE images and in some cases may exhibit an increased strain ratio corresponding to that for malignant forms. Such misinterpretation is related to the absence of the stress control during the US-SE imaging. For certain spatial distributions of mechanical inhomogeneities, the stress may become enhanced in the lesion vicinity, so that the nonlinearity of the tissue leads to uncontrollable increase in the Young’s modulus of the lesion, and, in the visualized strain ratio. Consequently, even for benign lesions, the observed in US-SE images strain ratio may increase up to levels typical of malignant tumors.

In contrast to the absence of stress control in US-SE, the used realization of C-OCE with pre-calibrated reference layers makes it possible to estimate the local stress applied to the tissue during its deformation. This allows one to quantitatively estimate the tangent Young’s modulus for the same chosen stress. Consequently, stiffness can be much more reliably estimated, compared and interpreted in different experiments (or in one measurement in which strongly inhomogeneous stress distribution occurs over the scanned region). In the described OCE-examinations the tangent modulus was estimated as the slope of the chord of stress-strain curves between the stress levels 2 ± 1 kPa (i.e., the central stress point is 2 kPa). Due to this stress control C-OCE results clearly demonstrated that the Young’s modulus for this lesion was significantly lower than for malignant tumors and corresponded to benign fibroadenomas. In more detail the quantified differences will be described in Section 3.5.

Continuing the discussion of examples related to misinterpretation of US-SE images, the next Fig. 6 shows the opposite situation, in which the high-grade ILC was diagnosed as a benign lesion based on US-SE strain ratio (see Figs. 6(a) and 6(b)). In the structural image (Fig. 6(a)) this lesion looks as low-echogenicity zone (labeled as A). In the strain image the increase in stiffness in this zone is not very pronounced, so that score 2 was assigned to this lesion with a mosaic pattern of green, red and blue (Fig. 6(b)). The strain ratio for zone A and reference zone B in Fig. 6(b) equals 2.2, which is typical of benign lesions. Although this diagnose was confirmed by several independent ultrasonic examinations, a fine needle aspiration biopsy was performed which indicated the presence of malignancy that required surgery.

 

Fig. 6. Infiltrating lobular carcinoma (grade III) of a 57-year-old woman. (a) B-mode ultrasound shows hypoechoic lesion (green circle). (b) is the US-SE image, score 2 for lesion with a mosaic pattern of green, red and blue (assessed as benign), with a strain ratio of 2.2. (c) is the corresponding C-OCE image showing a stiff lesion with dominating stiff component (over 600 kPa) and minor inclusions with low stiffness values (∼200 kPa and lower). (d) Histological image of the surgically excises specimen stained with H&E in which agglomerates of tumor cells intermittent with fibrous stroma and hyalinosis of single collagen fibers in central parts of tumor. The dashed line in Fig. 6(b) shows the cross-section at which the OCE examinations was made and then histological slices were prepared. Abbreviations: FS — fibrous stroma, TC — cluster of tumor cells

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C-OCE images (Fig. 6(c)) obtained for the excised tissue show a stiff lesion with a non-uniform distribution of high (over 600 kPa) stiffness values intermittent less stiff inclusions (200 kPa and even lower). In agreement with the histological slices made for the same section (Fig. 6(d)), the C-OCE images in Fig. 6(c) clearly demonstrate areas of the agglomerates of high-grade tumor cells with increased stiffness, as well as the presence of stromal component in central parts of tumor with significantly lower stiffness.

The reason of fairly low strain ratio indicated by US-SE evidently is again related to the absence of local stress control. In this case there were rather soft regions (large red spots above the lesion in Fig. 6(b)) above the lesion, their strong deformation during the compression, reduced the stress applied to the elastically nonlinear lesion, which is turn resulted in apparently lower values of the lesion stiffness and reduced the value of the strain ratio.

3.4 Comparison of US-SE and C-OCE imaging in the characterization of high- and low- grade invasive breast cancers

In this section we present examples of US-SE and C-OCE imaging related to detection and differentiation of malignant breast lesions. Figure 7 shows an example of a higher malignancy tumor that was correctly diagnosed by US-SE and C-OCE (Fig. 7). On US-SE image the strain ratio of 3.1 corresponded to an elasticity score of 3 and was interpreted as grade III cancer (Fig. 7(b)). The corresponding C-OCE-based stiffness map in Fig. 7(c) demonstrate clear correspondence with the histological slice shown in Fig. 7(d). On the histologic analysis (Fig. 7(d)), the well-defined homogeneous zone of high concentration of cancer cells with strongly elevated stiffness in the C-OCE-images (see the central part of Fig. 7(c) obtained by stitching several OCE scans).

 

Fig. 7. High-grade (grade III) IDC of a 64-year-old woman. (a) is B-mode ultrasound image in which the lesion looks as hypoechoic region (green circle A). (b) is the US-SE image in which the lesion looks as a fairly stiff zone with blue color in the middle and green at the periphery with an elasticity score of 3 (probably benign) and strain ratio of 3.1. (c) is the C-OCE image in which the lesion looks as a high-contrast stiff zone with the Young’s modulus >600 kPa. (d) is the corresponding histological image (H&E stained) in which the large agglomerate of tumor cells is clearly seen in the center surrounded by inflammatory cells and adipose at the peripheral zones. The dashed line inside the green circle A in panel (b) shows the direction along which the C-OCE scan and the histologic were obtained. Abbreviations: A — adipose, TC — cluster of tumor cells, LI — lymphocytic infiltrate

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In can be pointed out that in the C-OCE image the ratio between the Young’s modulus in the central part of the tumor and adipose at the periphery is ∼5–7, i.e., about twice higher than the strain ratio in the US-SE image. Similarly, to the above-discussed examples in Section 3.3 this difference is related to the fact that in the C-OCE examinations stiffness maps are obtained for a standardized stress over the entire image, whereas in the US-SE examinations there was no stress control. Therefore, the US-SE strain ratio could noticeably differ from the actual ratio of the Young’s moduli in the compared regions. Furthermore, in US-SE the choice of the reference region in the peritumor zone may additionally noticeably affect the estimated strain ratio.

Another important feature of C-OCE image is the very high contrast between the cancerous region and normal adipose. The tumor boundary on C-OCE images can be very well localized within a scale of 1–2 mm with an accuracy similar to segmentation of conventional histological images. However, in contrast to histology the C-OCE examinations are made without any special preparation of freshly excised samples and require only several minutes. These features of C-COE suggest that C-OCE visualization can be made intraoperatively and play the role of express biopsy feasible intraoperatively.

The next example shown in Fig. 8 relates to low-grade IDC which in US-SE image looked as fairly homogeneous stiff lesion with an elasticity score of 5 and strain ratio of 4.1 (see Fig. 8(b)). It is interesting to point out that on the C-OCE image with much higher resolution the tumor looked mechanically rather inhomogeneous, with clearly seen zones of very high Young’s modulus (∼1000 kPa) with penetrating fibrous streaks having significantly lower stiffness (Fig. 8(c)). On the histological image this elastographic structure revealed by C-OCE clearly corresponded to agglomerates of tumor cells embedded into fibrous stromal tissue (see Fig. 8(d)).

 

Fig. 8. Low-grade (grade II) IDC of a 68-year-old woman. (a) in the B-mode ultrasound image showing the lesion as hypoechoic zone (green circle A). (b) is the US-SE image in which the lesion looks a stiff zone with score 5 (malignant). (c) is the C-OCE image showing the lesion as a zone with a non-uniform distribution of intermittent high-stiffness (>600 kPa) and moderate-stiffness zones (∼200–300 kPa) in the center of the tumor node and soft surrounding non-tumor tissue with stiffness <200 kPa. (d) Is the corresponding H&E-stained histological image which shows the heterogenous lesion structure with clusters of tumor cells intermittent with fibrous stroma and hyalinosis with the transition to non-tumor fibrous tissue and adipose at the peripheral zones. The dashed line inside the green circle in panel (b) shows the direction along which the C-OCE and histology images were obtained. Abbreviations: A — adipose, FS — fibrous stroma, TC — cluster of tumor cells

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Similarly, to Fig. 7(c) in the C-OCE image in Fig. 8(c) the margins between normal (peri-tumoral) tissue and the invasive tumor are clearly seen. The OCE images in Fig. 8(c) very clearly show the margins of the breast cancer as high-contrast zones with strongly increased stiffness surrounded by lower-stiffness fibrous tissue and especially soft adipose tissue of the mammary gland, which well agrees with the histological images shown in Fig. 8(d).

The comparison of the histological images with C-OCE scans in Fig. 8(c) and Fig. 7(c) demonstrates high utility of C-OCE imaging for intraoperative detection of tumors having both high and low grades of malignancy. Much higher than for US-SE spatial resolution of C-OCE imaging (reaching tens of micrometers) clearly show the differences in the morphological structure between tumors of different morphological types. As already mentioned, the high spatial resolution of C-OCE and high contrast between peritumoral zone and central zone of tumor in combination enable very clear visualization of the tumor margin comparable in accuracy with tumor segmentation on histological examinations.

Overall, the above consideration of various breast lesions confirmed that the C-COE elastographic imaging is very promising for distinguishing of benign and malignant breast lesions with much higher contrast than it US-SE images. Consequently, C-OCE bodes well as an intraoperative tool for express differentiation between benign and malignant lesions, assessment of malignancy grade and detection of clean boundary of tumor excision with an accuracy comparable to that of conventional laborious and time consuming histological examination.

3.5 Diagnostic performance of US-SE and C-OCE in the differentiation of benign and malignant breast lesions of various grades

In this section we summarize the results of the complementary US-SE and C-OCE examinations of breast-tissue lesions. We recall that these two techniques yield only indirectly related quantities: for US-SE, the relative strain ratios are obtained without the possibility to control stress exerted on the tissue, whereas for C-OCE, the quantified Young’s moduli obtained for the chosen local stress. Another key point that should be pointed out is that for the possibility to detect/differentiate the lesions, separation of the entire sets of data (strain ratios for US-SE and stiffness values for C-OCE) among diagnosed lesion types should be ensured. This requirement is strongly different from that in some other applications (e.g., for comparing efficiencies of different therapies), for which it is often quite sufficient to show statistically significant difference in the mean values, even if the distributions of these data around the mean values may significantly overlap.

 

Fig. 9. Summarized results of US-SE and C-OCE examinations. Panel (a) shows the strain ratios estimated by US-SE and (b) is the mean stiffness on C-OCE images for benign and malignant lesions of breast tissue. For fibroadenoma with a limited number of data of our US-SE examinations (n = 5 filled circles), we added n = 6 other points from literature [28,49] (empty circles) to demonstrate that scattering or strain ratios for fibroadenomas may be very broad, strongly overlapping with data for malignant tumors. Abbreviations: IDC — infiltrating ductal carcinoma, ILC — infiltrating lobular carcinoma. n = number of images

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Figure 9(a) shows the strain ratios obtained by US-SE before surgery and Fig. 9(b) presents the stiffness values determined by C-OCE for the freshly excised tissue of the same lesions. For better visual impression, the data points for each lesion type are slightly separated laterally. For each cloud of the data, thick horizontal line shows the corresponding mean value of the corresponding data points. The thin vertical bars around the mean value show the standard deviation, the latter by the definition being smaller than the total data scattering in every group. For the US-SE data shown in Fig. 9(a), all lesions (both benign and malignant) demonstrate strain ratios clearly higher than unity. In our pilot study we had only five points for fibroadenomas (filled blue circles), of which a single point demonstrated significantly elevated strain ratio ${r_s}\sim 3.9$ (this case was discussed in Fig. 5 as an example of fibroadenoma incorrectly diagnosed as a malignant lesion). To show that such an outlier point is not due to incorrectly determined strain ratio in our particular experiment, we added some other points (empty blue circles) taken from literature [28,49] to show that strain ratios for fibroadenomas indeed may demonstrate very strong scattering and even significantly overlap with the strain ratios for malignant tumors. Next it can be mentioned that all 3 groups of the malignant lesions demonstrate strain ratios clearly exceeding unity, but at the same time an evident feature is that for lesions with higher malignancy grade, the mean strain ratio demonstrates pronounced decrease (note that similar decrease in the strain ratio for high-grade tumors was independently reported, e.g., in [49]). As is clear from Fig. 9(a), for especially aggressive ILC tumors (3rd grade of malignancy), the strain ratio decreases down to the values typical of benign fibroadenomas. This may easily cause misinterpretation as in the examples given in Figs. 6 and 7. This overlap of the strain ratios for benign and malignant lesions is clearly seen even for the fairly limited amount of data in this study, and for a larger number of samples this overlap will only further increase. Consequently, without accounting for additional features (such as echogenicity, geometry, etc.) the differentiation of various lesion types based on such strongly overlapped strain ratios given by US-SE may lead to a significant portion of erroneous conclusions.

For the C-OCE data shown in Fig. 9(b), the first observation is that the estimated modulus for the same fibroadenomas demonstrate visually smaller scattering in the estimated absolute values of stiffness. However, the relative scattering, i.e. the ratio of minimal to maximal stiffness determined by C-OCE is quite similar to the range of strain ratios given by US-SE and shown in Fig. 9(a) for fibroadenomas. However, unlike this similarity a striking difference between Figs. 9(a) and 9(b) is that the there is no overlap of the absolute values of stiffness for fibroadenomas and for all 3 groups of malignant lesions (that are several times stiffer than fibroadenomas). Another striking difference is that for tumors of grade I-II, the stiffness values determined by C-OCE are clearly smaller than for grade III, although the strain ratio given by US-SE for grade I-II, is, in contrast, noticeably higher than for grade III types.

These differences between the US-SE and C-OCE results are due to different measurement conditions for the two methods. Once reason is that in the used C-OCE realization for all types of lesions, the reference material was the same linearly elastic silicone. In contrast, in US-SE the strain in the supposed tumor is compared with the strain of the peritumoral tissue, the properties of which may noticeably vary. Even if this peritumoral zone does not contain stiff agglomerates of cancer cells, the morphology of this tissue around malignant tumors may be significantly altered (there is a stronger proportion of stromal tissue with the stiffness noticeably higher than for adipose). This elevated stiffness of peritumoral zones around malignant tumors has been confirmed by shear-wave USE and certainly this stiffening of the peritumoral zone reduces the strain ratio obtained by US-SE for malignant tumors [50,51]. Another reason that may reduce the strain ratio for malignant tumors in US-SE is the lower resolution than in C-OCE and much larger size of the area (usually 10 × 10 mm), over which the strain for tumors is estimated. This area may easily cover some portion of softer vicinity of the tumor. In contrast, in C-OCE measurements, the resolution is higher and averaging window sizes are significantly smaller (∼ several mm laterally and ∼0.5–1 mm in depth), so that the stiffness has been estimated for the tumor nodes excluding surrounding softer tissue, because tumor boundaries are very clearly seen in C-OCE images as shown in Figs. 6, 7 and 8. Thus, the stiffness value presented in Fig. 9(b) for fibroadenomas and malignant tumors are genuine without contribution of peritumoral tissues.

Finally, it can be emphasized that the C-OCE estimates has been obtained for a standardized stress (2 ± 1 kPa in this study). In contrast, in US-SE there is no stress control (although it is almost for sure that stress applied to the tissue by the fairly large US-probe was smaller than for C-OCE measurements). This is also an important factor, because tumors are elastically very nonlinear (examples of nonlinear stress-strain curves can be found in [3,15,16]), such that even for rather moderate stress ∼several kPa, the tangent elastic modulus may increase several times from its initial value. At the same time, nonlinearity of adipose and even fibrosis is significantly lower, so that, for the same stress, their stiffness is not so strongly increased as for cancerous tumors. Due to this difference, C-OCE measurements performed at a moderate stress of several kPa enable significantly higher contrast in stiffness for malignant tumors. It can also be pointed out that both US-SE and C-OCE data consistently show that for ILC tumors, the mean stiffness is slightly lower than for IDC tumors, although the scattering is comparable with the difference in the mean values for these two types of tumors.

The above-mentioned differences between the US-SE and C-OCE manifest themselves in their diagnostic performances. Although in the present pilot study the amount of data is too limited for high-confidence comparison of diagnostic performances of the two techniques, even for the available data, it is instructive to compare sensitivity and specificity and give estimates of the area under the receiver operating curve (AUC) for the two methods. These results are summarized in Table 1 (in which the US-SE data for fibroadenomas from literature are not used).

Table 1. Diagnostic performances of US-SE and C-OCE for the diagnosis of benign and malignant breast lesions calculated using only the data available in this pilot study

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In agreement with Fig. 9(b), where fibroadenomas demonstrate clear separation from the malignant lesions without overlap, the C-OCE yields 100% values for both sensitivity and specificity in differentiation of benign and malignant lesions (with the duly chosen threshold > 334 kPa). For US-SE and optimal strain ratio threshold >2.5, both the sensitivity and specificity were significantly lower (∼80–84%). Concerning the differentiation of grade I-II and grade III cancers, both strain ratio in US-SE and mean stiffness in C-OCE may give comparable high results. Concerning the differentiation of benign and malignant lesions using US-SE, the accuracy may be improved if, in addition to strain ratios (that noticeably overlap for fibroadenomas and ILC lesions), some additional information (like echogenicity features for these lesions) is used. Concerning C-OCE it can also be mentioned that for differentiation of grade I-II lesions from grade III lesions, the accuracy can be significantly improved using only elastographic data, if in addition to the mean stiffness values the inhomogeneous stiffness distribution in stiffness maps (demonstrated in Fig. 8(c)) is taken into account.

It should be also clearly understood that straightforward comparison of apparently the same parameters of sensitivity and specificity presented in Table 1 is not very meaningful because the areas of applications for the two compared techniques are essentially different. Namely, the ultrasound examination is intended for in vivo applications on patients for preliminary non-invasive detection of suspicious lesions and guidance for subsequent obtaining of tissue samples for histological examination and surgical intervention in necessary cases.

In contrast, in a certain sense similar to histology, C-OCE is intended for examination of excised breast-tissue samples, including the possibility of nearly real-time intraoperative application. For such applications, of special importance is the ability of C-OCE to improve both sensitivity and specificity of detection of malignant tumors and to efficiently differentiate low- and high-grade tumors (especially of grade III).

Therefore, evaluation using quantifiable C-OCE features showed better diagnostic performance than conventional US-SE in breast lesion differentiation. Based on the C-OCE images, the absolute values of malignant and benign breast lesions stiffness can be estimated during surgery and used for differentiation of tumor grades and determining a clear resection margin in BCS. Probably this ability of C-OCE to very clearly visualize tumor boundaries, nearly in real time and with an accuracy comparable to that of histological examination is of the most important for practice.

4. Discussion and conclusions

In this work, by analogy with the recent comparison [14] of wave-based US elastography and wave-based OCE, we compared compression-based US-SE and compression OCE. Besides the preliminary verification of the similarity of strain-ratio estimates for linearly-elastic and homogeneous phantom samples, for the first time we compared the results of US-SE and C-OCE for assessing the same set of various of breast lesions. In this study we focused on the influence of elastic nonlinearity and mechanical inhomogeneity of real tissues on the result of the two techniques, beyond the difference in their resolution and penetration depth. We demonstrated that in comparison with US-SE, the compression OCE has novel capabilities due to the realization of local stress control and the possibility to perform spatially-resolved mapping of stress-strain curves and estimate the tangent Young’s modulus in heterogeneous tissues. Due to usage of reference silicone layers this modulus is estimated for the same pre-chosen level of the stress applied to the tissue [16].

Besides, the basic assumption in the compression-elastography about fairly uniform uniaxial stress near a solid piston pressed onto the tissue [52] holds fairly well for C-OCE, because the imaged depth is significantly smaller that the OCT-probe diameter. All these features of C-OCE ensure meaningful comparison of quantitative OCE data obtained for real nonlinear tissues in different experiments and for different samples.

In contrast to quantified Young’s modulus in the described realization of C-OCE, conventional US-SE technique gives only relative data (strain ratio) obtained without controlling the level of the created stress, although the latter may noticeably deviate from uniform within the imaged region, especially at distances comparable with US-probe diameter. Along with tissue nonlinearity this stress inhomogeneity may contribute to additional ambiguity. Furthermore, US-SE uses the peritumor tissue as the reference material, although even outside tumors the elasticity of non-tumorous tissue may noticeably alter its stiffness (in particular, the elasticity of “normal” tissue may increase in the vicinity of high-grade tumors [49,50]). This fact may also affect the strain ratio obtained by US-SE and cause its reduction for high-grade tumors in comparison with the case of low-grade tumors. For example, in Fig. 9(a) for grade III tumors, the US-SE strain ratio is smaller than for grades I-II, even if the genuine Young’s modulus for grade III tumors is higher than for grades I-II as is clear from Fig. 9(b). Note that it was also shown in [53] that, for localized inclusions (close to spherical or cylindrical), the observed contrast in strains under compression is smaller than the contrast in the Young’s moduli between the inclusion and surrounding tissue. This effect may also lead to reduced strain ratios for localized stiff grade III tumors imaged by US-SE.

Overall, the range of elasticity scores found in this study, as well as the mean values of strain ratios given by US-SE, are consistent with those in previous studies [26,30]. These results confirm that US strain elastography without local stress control enables essentially qualitative/relative information, which complicates quantitative comparison among various cases [54]. The above mentioned distorting factors could be responsible for the fact that of 4 benign cases diagnosed by US-SE one case proved to be malignant according to both our C-OCE results and histology. Also, among 18 malignant cases consistently diagnosed by histology and C-OCE, two cases were erroneously evaluated by US-SE as benign.

Note also that intraoperative ultrasound has been recently used as a guiding tool in breast-conserving surgery (BCS) to locate the tumor position and assess breast tumor margins [55,56]. However, this method is not sufficient to detect isoechoic small lesions and its resolution does not suffice for detecting tumor margins within 1–2 mm. In this regard we demonstrated that C-OCE images very clearly show the margins of the breast cancer as high-contrast zones with strongly increased stiffness in comparison with the surrounding softer fibrous tissue and especially adipose of the mammary gland. The examples of C-OCE images in Fig. 7(d) and Fig. 8(d) demonstrate a very good agreement with the histological images. We also showed that C-OCE enables better sensitivity and specificity in the detection and differentiation of benign and malignant lesions, as well as in differentiation of low-grade and high-grade malignant tumors (see Fig. 9 and Table 1).

The main limitation of in vivo OCT imaging is its limited depth of visualization of 1–2 mm, which impedes the examination of the entire thickness of the tumor node. Overcoming (at least partial) of this limitation is possible due to examination of excised post-surgery samples (as in the present study), as well as by utilization of endoscopic probes and catherers [57,58].

Overall, the reported results confirm high potential of C-OCE as a high-speed and accurate method for breast tumor margin evaluation and express assessment of the lesion grade. In contrast to histology such C-OCE examinations can be made intraoperatively on a scale of minutes without special preparation of the tissue samples. Further progress in the development of C-OCE technique and creation of portable, affordable and easy to handle OCE-devices enabling real-time high-resolution elastographic imaging should be an important aid in realization of BCS with the maximum possible perfection.